^ecltnlcciL ^coie

PB 16)575

74

SCATTERING OF COBALT-60 GAMMA

RADIATION IN AIR DUCTS

U. S. DEPARTMENT OF COMMERCE

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technical ^^ote

74

OCTOBER 1960

SCATTERING OF COBALT-60 GAMMA

RADIATION IN AIR DUCTS

Charles Eisenhauer

The work described in this Technical Note was sponsored

by the Office of Civil and Defense Mobilization, the Bureau

of Yards and Docks, Department of the Navy, and the Defense Atomic Suppoit Agency, Department ofDefense.

NBS Technical Notes are designed to supplement the Bureau's regular publications program. They provide a means for making available scientific data that are of transient or limited interest. Technical Notes may be

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Scattering of Cobalt-60 Gamma Radiation in Air Ducts

Charles Eisenhauer

The exposure dose rates due to Cobalt-60 gamma radiation

scattered in small air ducts in concrete has been measured for

ducts with one and two right angle bends. The inside corner of

a right angle bend has been found to be an important source of

scattered radiation. Results are analyzed in terms of solid angle

relationships and attenpts are made to extrapolate experimental re- sults to other duct configurations.

1. Introduction

Although the scattering of nuclear radiation in air ducts within

a shield is a common problem, the tendency has been to treat only

specific duct configurations. For example, designers of reactor

shields have been concerned with the penetration of radiation from

reactors through beam ports and other relatively small ducts in the

reactor's biological shield. On the other hand, designers of radiological shelters have been concerned with the penetration of radiation from nuclear weapons through the much larger entranceways associated with shelters. More recently, with the advent of high intensity gamma ray sources, calculation of the scattering of gamma

radiation in passageways leading from the source chamber to the sur- rounding environment h^as become an important problem. The proper

design of ducts over this large range of configurations requires a more detailed knowledge of the scattering processes in a duct. Accordingly, an experimental investigation was undertaken to study the

scattering of Cobalt-60 gamma radiation in air ducts in concrete.

Ducts with one and two right angle bends were studied. The investigation was restricted to ducts with a uniform cross sectional area.
2. Experimental Arrangement

Measurements were made on small (less than 1 square foot area)

air ducts in a concrete medium. A typical duct configuration with

the overhead shielding blocks removed is shown in figure 1. The

duct shielding consists of solid concrete blocks with an average

density of 124 pounds per ciobic foot. In all measurements, the

distance from the source to the geometrical center of the first

junction was 100 centimeters. The experiment was run for three different duct cross sections; namely, 19.2 cm x 19.2 cm, 28.2 cm x 28.2

cm, and 19.2 cm x 28,2 cm. The source used in this experiment was a collimated Cobalt-60 source of 1 curie nominal strength replaced

later by one of 4- curies. When a lead plug was removed from the

lead source-container the radiation from the gamma source was emitted

within a cone of half angle, a> such that tan a = 0.3. (See

figure 2.) Under these conditions radiation strikes the walls of

the 28.2 cm duct, for example, about half-way down the duct and

therefore the junction in all cases is well illuminated by the source

radiation.

The detectors used in this experiment are shown in figure 3.

The two chambers on the right are the non-self-reading Victoreen

Model 362 pocket ionization chambers which are used very frecpjently

in personnel protection. These chambers are useful in the dose

range of 20 to 200 mr. For low intensity levels we used the larger

cylindrical chamber 3 inches high and 2 inches in diameter, shown

on the left. The latter is useful in the range of 1 to 10 mr. All

readings in this experiment were made on the Victoreen minometer

type of electrometer shown in the figure.

All measurements were taken with the axis of the chamber

perpendicular to the plane formed by the axes of the two legs of

the duct. The chambers were supported in the aluminum holder shown

in figure 3. The center of the chamber was taken as the effective

detector position.

Measurements by Day [l] indicate that the energy response of

the pocket ionization chambers is uniform down to about 250 kev.

More recent measurements by Sanders, Auxier, and Cheka [2] confirm

this and also indicate that the directional response of the pocket

ionization chambers is isotropic for radiation in^inging at angles

from 30° to 90*^ with the axis of the chamber. The response de- creases from a response of unity at 30° to a response of l/2 at 0°

(radiation parallel to the axis). They found, furthermore, that

the addition of J+O mils of tin on the cap-end of the chamber improves the energy response making it uniform down to about 50 kev

and at the same time makes the angular response of the detector

more nearly isotropic for low energy radiation.
The tin absorber was used in this experiment to check for

spuriously high readings due to the presence of low energy radiation.

It is shown in place on the middle chamber in figure 3. Readings

taken with the 200 mr chambers at D = 20 cm and D = 50 cm indicated

a difference of less than 5% with and without the tin absorber. This seems to indicate that there is no significant component of low

energy radiation, but rather that the bulk of the radiation present

is concentrated about an energy of ~ 350 kev, corresponding to a single scatter of 90°.

Measurements by the Anny Chemical Center [3] on the 10 mr dosimeters indicate that they are even more isotropic in response than

the pocket ionization chambers. Although no energy response measurements have been taken on the 10 mr chambers, dose rates measured at

several points both with the 200 mr chambers and the 10 mr chambers

show good agreement.

3. Results

"3.1 Single Bend

The segment of the duct between the source and the first bend

will be referred to as the first leg of the duct. The attenuation

in the first leg of the duct is not discussed here because it is so sensitive to the angular distribution of the source radiation. For

example, if the source were a parallel beam then there would be no attenuation at all in the primary leg since the dose rate at the

entrance of the first leg and at the junction would be the same. On

the other hand, if the flux at the entrance to the first leg is an

isotropic flux then the dose rate from unscattered radiation at any

point along thfe primary leg of the duct will be inversely proportional to the square of the distance from the source. It is assumed,

therefore, in this paper that the dose rate at the first junction of

the duct can be either measured or calculated for the particular

source geometry involved.
The measured exposure dose rates along the central axis of the

second leg of the duct are shown in figure 4 for three different sized

ducts. The distance D is measured from the geometrical center of the

duct junction to the effective detector position. The first trend

that became apparent in this experiment was that the dose rate in the

second leg of the duct varied more nearly as ~^ rather than as —**r

2 (This is shown in figure 5.) A i/D variation can be interpreted as

a simple solid angle relationship since the solid angle, Q, approaches

HW ' for D much larger than the height H and the width W of the duct.

The solid angle would be that subtended at the detector by a hypothetical plane radiator of area HW located at the center of the

junction, noimal to the axis of the second leg of the duct.

3.2 Effect of Corner

It is important to know which wall surfaces of the junction are

the most important secondary sources of scattered radiation. If we assume that the two walls foiroing the outside corner of the junction

are the most important secondary sources, and that they contribute

about equally, then setting back one of the walls to form a radiation

trap should reduce the dose rates in the second leg by about 50%.

Setting back one wall about a mean free path, however, produced only

about a 15% decrease in dose rate. Further investigation showed that

this was because scattering in the inside corner of the junction accounted for about half of the dose rate and was therefore unaffected

by setting back the walls of the junction. This was a rather un- expected result. The 'concrete of the inside corner of the junction

and the rear wall of the second leg (the wall nearest the source) was replaced with Pb and the measurements were repeated. Results are

shown in figure 6. Tests showed that most of the difference was due

to the Pb which was within 6 inches of the corner. Since the lead

and concrete blocks were not co-modular, the duct geometry with the

lead corner was somewhat distorted and therefore different frcan the

original gecaietry. The error due to this distortion is not expected

to be greater than about 20^. Nevertheless, the measurements with

Pb should be considered only as a qualitative estimate of the effect

of the corner contribution.
The relative contribution from the corner should decrease as the duct size increases. This can be seen from the following argument. The dose rate at a fixed distance from the junction due to the

corner scatter will be approximately proportional to the duct height

(~ H) , while that due to- reflection from the junction walls will vary

as the area of the duct (~ H x W). Therefore, for large ducts

(HqW/2 » l) the ratio of the corner contribution to the reflected

contribution approaches zero. Here [i^ is the mean free path in the

s,u,r, r,oun(ij.,n,q medium.

3.3. Double Turn

The dose rate in a duct having two right-angle turns was also

investigated. The dose rates in the third leg are presented in

figure 7 as ratios of the measured dose rate R, to the dose rate R

at the center of the second junction. The ratios were measured for

the case of two right angle turns of the same sense ( [ \ ) and

two turns of the opposite sense ( • ,

, [ ) . Shown for comparison

is the dose rate in the second leg relative to the dose rate at the

first junction plotted against distance from the first junction. It

is seen that the behavior is very different both in magnitude and in

rate of decrease with distance. The ratios for distances of less

than 14.. 1 cm correspond to locations which are within the junction.

They therefore follow the trend of the dose rates in the leg precedina the junction. Thus, the dose rate ratio, in the case of the

(• J ) duct, increases at first, due to the distribution in the

second leg, and then decreases when the detector is located beyond

the junction in the third leg of the duct.

4.. Discussion

We now look for an analytical expression with which we can fit

the experimental data. We know that each wall of the junction including the inside corner, contributes to the dose rate in the

second leg. One approach is to calculate the contribution from each

wall and the corner separately. This approach is being tried by

J. C. LeDoux [4] at the Naval Civil Engineering Laboratory using the

albedo data generated by Berger and Raso [5]. We prefer, however, to

look for a composite expression which includes the corner contribution

and thus describes the total radiation received at the detector.

This expression should be valid for large and small ducts alike.
In the past it has been generally assumed that the dose rate

should be proportional to the solid angle subtended at the detector

by the junction. The ratio of the dose rate R at the detector to

the dose rate R^ at the center of the junction can then be written

as R/Rq = ka)

where k depends on the characteristics of the junction but not on

the detector position. In order to calculate the solid angle co, the

junction must be replaced by a hypothetical radiating area at a distance D from the detector. It has never been clear, however, how

this distance should be defined. In our experiment we find that if we measured distance from the center of the junction, the dose rate

varies as ""^ . We now ask if there is any way of defining the ^

1 distance such that the dose rate will vary moi-e closely with ~~r and

thus be proportional to solid angle. After investigation we found

that we could do this by defining a new distance D' which is equal to

The choice of such a definition can be justified by reference to

figure 8. For a large duct (W » l/p.) the distance D' is effectively

the distance from the exit face of the junction. For a small duct,

however, D' is the distance from a plane located one mean free path

into the second leg. Thus the inside corner is recognized as an

integral part of the junction.

The expression for the solid angle fraction (see reference 6),

CO = ~"^> subtended by a rectangle is

2Tr

co = -2-tan-l ^

IT T]v T) +e +1

where e and r\ are two eccentricity parameters. Their values in teims

of the parameters of this report are

e = w/H and

Tl = 2 D/H

We have calculated o) as a function of D', substituting D' for D in

the formula for t]»
A plot of the measured ratio -r- against oo is shown in figure 9

"o

for a duct with one right-angle bend. From the observed linear

p relationship we may say that "-r~ is equal to k x o) where

k = 0.095 ± .005. The subscript 1 on k refers to the first junction.

Furtheimore, if we compare this expression with data taken on large

p ducts at Brookhaven National Laboratory [7] we find that —r— = k' 00, "o

where k' differs from k by only 20%, The data taken at Brookhaven

are also shown in figure 9. It should be noted that this behavior applies only to point sources where the value of the source-to-junction

distance is large compared to the width of the first leg. There is some evidence from Brookhaven that the behavior of the dose rate in

the second duct will change if the source-junction distance is reduced

significantly.

We now ask how the constant k, might vary for other kinds of

ducts. In this discussion we take the approach that the radiation

reaching the detector is singly scattered radiation from scattering

centers in the walls of the junction. The energy scattered at angle

is then equal to the product of the average fraction f(E ) of energy

retained by the scattered photon in a collision and the fraction

p(cos0) of the scattered energy radiated at an angle 9:

k^ = f(E )p(cose)
As an approximation we assume that the angular distribution of

scattered energy assumes the angular distribution of the energy of

singly-scattered Compton photons

p(cos0)«K(e) = 2frE(cos0)-^(cos0)|J E(cos0' )-^(cose')dQ'|

where E(cos0) is the energy of singly scattered Compton radiation,

.^ is the Klein-Nishina differential cross section for a dQ

scattering angle 0, and the constant Zw is a conversion from solid

angle Q, to solid angle fraction oo. K(0) is shown in figure 10 for

Eq - 1.2 Mev. We then expect that in ducts with bends of angles

other than 90° the intensity as a function of the duct angle should

follow this relationship. The horizontal line at p(cos0) = l/2

gives the result for an isotropic angular distribution. Also, shown

for comparison is the (sin0)~-^ trend which has been assumed in the

past [8] as the dependence on the angle of the bend at the duct. It

is seen that the Klein-Nishina formula predicts a more severe variation with angle. The value for 90° is 0.17. The average fraction,

f(Eo), retained by the photon has been calculated by Nelms. [9] For

Cobalt-60 the value is f = 0.53. Thus, the value of k predicted from

these considerations is

k^ = (0.17) (0.53) = 0.090

in close agreement with the value obtained from these measurements.

8
Let us now look at the dose rate variation in the third leg of

the duct. The dose rate ratios for the two types of right angle bends

are shown in figure 11. The solid angle co is now computed in terms of

a distance D" given by

d" = D - -^ -

,

where "^ is the mean free path corresponding to the average energy

(~ 350 kev) of radiation in the second leg. Although the dose rate

ratio in the third leg is approximately proportional to coj the absolute

value is much greater than that in the second leg. The dose rate ratios

are given by

r/rq = o.sco (<—

r

case

and

R/Rq = 0.5a) ( 1 J case

The difference in magnitude between these two cases for values of o)

near unity is a consequence of the dose rate distribution in the second

leg. Although parallel lines have been drawn through the two sets of

data) it is not clear whether or not the two sets of data would approach each other for very small values of co.
The second junction has an apparent albedo which is five to

eight times greater than that of the first junction. Care must be

taken, however, in the interpretation of these numbers because the

reference dose rate varies rather widely over the dimensions of the

second junction. For example, if the dose rates were related to the

measured dose rate R, at the entrance of the junction minus one mean

free path instead of Rq at the center of the junction, the new values

of k2 would be

Ro 3.71

k^^k^ —=0.8x3^=0.35 (<_

Rq 3.71

Revising the value of k, in a similar manner would yield

Rq 1050

k, = k, ~ = 0.095 X ^^ = 0.058

and the albedo for the second junction would now be four to six times

greater than that of the first junction. Thus the ratio of the apparent albedo of the first and second junctions is quite sensitive to

the manner in which the albedo is defined.

Following the reasoning used in the last section for predicting

k we calculate another K(9) distribution corresponding to a source energy of 350 kev and find that the value of K(e = 90 ) is 0.27.

The value from reference 9 for the fraction of energy retained by a photon of energy E = 350 kev is 0.71. The predicted value of k is

k^ = (0.27) (0.71) = 0.19

which is closer to the empirical value obtained when defined in terms

of the dose rate at the entrance to the junction rather than at the

center. A comparison of the predicted values of k and the experimental values obtained for each definition is shown in table 1.

1
Table 1

E>qperimen tal Predicted

k

R ^ X k'

R,

1. (0

k = f(E^)p(co

First bend Q.095 0.058 0.090

Second bend ( ^_—1 ) .80 .35 .19

( >^

.50 .22 .19

Although the predicted value of k for the second junction is more

consistent with the experimental values of k', the disagreement is severe enough to suggest further study. The predicted value of k for

the first junction however, is in good agreement with the experimental

value of k = 0.095.

5. Acknowledgment

The author wishes to thank Dr. L. V. Spencer for suggesting this

experiment and for many helpful discussions. Many thanks also to

R. Bach, 0. H. Hill, and Mrs. S. Ripps for technical assistance in

preparing this report.

1 1
6. References

[l] F. H. Day, X-ray calibration of radiation survey meters, pocket

chambers, and dosimeters, NBS Circular 507, (July 1951).

[2] F. W. Sanders, J. A. Auxier, and J. S. Cheka , A simple method of

minimizing the energy dependence of pocket ionization chambers,

Health Physics 2j No. 3, (Feb. I960).

[3] R. Rexroad (private communication).

[4.] J. C. LeDoux (private communication).

[5] M. J. Berger and D. J. Raso, Monte Carlo calculations of gammaray backscattering. Radiation Research 22, 1, (Jan. I960).

[6] L. V. Spencer, Structure shielding against fallout radiation from

nuclear vgeapons, (to be pijblished by Office of Civil and Defense

Mobilization, Washington, D.C. ).

[7] F. Rizzo (private communication).

[8] A. Simon and C. E. Clifford, The attenuation of neutrons by air

ducts in shields, QRNL Report 1217, (March 1954).

[9] A. T. Nelms, Graphs of the Compton energy-angle relationship and

the Klein-Nishina formula from 10 Kev to 500 Mev, NBS Circular

542, (Aug. 1953).

1 2
c

u) o ^ .H O +> O -H

f-H in Si o

a enC -\

•H nj "O o

.-I -H

0) a

0) C

(0

<U C

•? *

h o > (0 o

+-> f-< u

+> c

U 0) P o

-p

t-H (O

(0 p h

c o

(1) +> 6 o

•H <U

fH +>

<U <D CLQ

X

0)O <1>

0)a

a

(0o>a

•o

(0

0)

(0

0)u

uD

O

c

§

S +^ O "H

en
roO

II o

0)

•—Ia>c

-ac

tnoO

(0 QO

4-> U

0) +»

0) TJ

CT> C

•H3O

x:

(0 •

»-> c u o 3 .H

T3 +>

a> o

•H o >c o
M

0) TJ 0) -P

<U M <u +J Q) >. E

:3 6

cn o

Pi c

o to 0) •H e x: C 6 o

^ c

0) c fH 0) ^.2 o

Pi (0 -P w O

•53 +-> -P

CO o

•H 0) •H h C +J >

e o^ Pi Q> o ei X rH -P 4h -P

0)

<U J*i c c

x: o •H o

-P o +J a T5

CO X fO •H Pi +J CD a •H Pi -p 5

M-1 O 0) o S

Pi rH Oi OJ a S

4-> O a

< s (D CO H Pi Pi s CD •

0) i

C fH c <u

0) a> o X

6 T3 o

ar-i •V •H O c Q> D x: 3 X cr o H 0) s x:

13 CO c c • O .H o Cl> •H E CO CO +j 3 t-i c

O .-H CD o

<1> (U a +J 0) CO 0) c Pi Q} Q .H CO Pi
Fig. 4»

40 80 \) 120

DISTANCE FROM JUNCTION, cm

Measured dose rates vs distance from the center of the

junction. Results are shown for three ducts of different

sizes.
10

10

E

q:

(l/D)

m

(\/oy

O H =W=l9.2cm

A H =W=28.2cm

D H =28.2 cm, W=l9.2cm

r\

10

l/D, cm"*

Fig. 5- Measured dose rates vs reciprocal distance for three different sized ducts.
10^

10

v.e

1.0

— CONCRETE - y/////7//////

i

O SOURCE

CONCRETE

/jV

Detector

O TOTAL DOSE RATE

O

O

_ A

A

A

CONCRETE

—\ 1 : CONCRETE y//////////

V O SOURCE

Detector K^Tpj,

A DOSE RATE WITH CORNER

CONTRIBUTION EXCLUDED.

i

40 80

DISTANCE FROM JUNCTION, cm

120

Fig. 6. Measured dose rate vs distance showing the difference in

dose rates when the concrete corner is replaced by lead.

Data were taken for a square duct with H = W = 19.2 cm.
10

.oL^

R/R(

0.1

.01

D A O

D

a

a

—

A

Ro-*- jSOUNGb -

R •'detector

O p 1 X SOURCE —

• *- Ro

DETECTOR

Q

RoX SOURCE ~

1 R

DETECTOR

o

D

1

10 20 30 40 50

DISTANCE FROM JUNCTION, cm

Fig. 7. Dose rate ratios vs distance after one and two right angle

bends

.
o ^

-J

-! I

CO \\

•c)

0) •H

+Jo x: 3 -p -o (0Q.

0)a> 0)

»H 0) m ^

.—1fH

T3Cio

0)oc

0) c

OJ

0)B

0)u

a> x:3I

T3

C 5|Oi c O -H

•H I T3 i^ Q § C O ^ II M

<D - P Q Q (D

«0

•H
R/Ro

Fig. 9. Dose rate ratios vs solid angle fraction after one right

angle bend.
Q5

(A

O

O

COS 9

Fig. 10. Angular distributions of scattered energy from a beam of

radiation. The horizontal line refers to an isotropic distribution, K(9) is obtained from the Klein-Nishina formula

for Cobalt-60 radiation, and the third curve is a normalized

inverse sine distribution.
1.0 — o — R _ DETECTOR

— D

R/F\)"

.01

.01

SOURCE

SOURCE

X

R

9

DETECTOR

/ I

/ -

//

//

SECOND LEG

0.1 1.0

<JJ

Fig. 11, Dose rate ratios vs solid angle fraction after two right

angle bends. The dashed curve indicates the behavior in

the second leg (after one right angle bend"*.

USCOMM—DC